Consumed by school, say (5)
I believe the answer is:
'consumed' is the definition.
(similar in meaning)
'school say' is the wordplay.
'school' becomes 'eton' (famous UK public school).
'say' indicates a 'sounds like' (homophone) clue.
'eton' is a homophone of 'EATEN'.
'by' is the link.
(Other definitions for eaten that I've seen before include "Upset" , "Polished off" , "Scoffed" , "absorbed in the system" , "This bread is soon forgotten, it's said" .)